On complex dynamics from reversible cellular automata

TL;DR

This paper demonstrates that reversible cellular automata can generate complex behaviors by adding random states, showing that reversibility is a useful structure for creating complexity in cellular automata systems.

Contribution

It introduces a novel approach where complexity arises from reversible cellular automata through the addition of random states, expanding the methods for designing complex cellular automata.

Findings

Complex behaviors emerge when adding about twice as many random states as the original states.

Reversible cellular automata can produce complex dynamics with dozens of states.

Operations like state permutations also facilitate the emergence of complexity.

Abstract

Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing instances of complex cellular automata; however, most of the proposed methods are based on a careful search or a meticulous construction of evolution rules. This paper presents the emergence of complex behaviors based on reversible cellular automata. In particular, this paper shows that reversible cellular automata represent an adequate framework to obtain complex behaviors adding only new random states. Experimental results show that complexity can be obtained from reversible cellular automata appending a proportion of about two times more states at random than the original number of states in the reversible automaton. Thus, it is possible to obtain complex cellular automata with dozens of states. Complexity appears to be commonly obtained from reversible cellular automata, and using other operations such as permutations of states or row and column permutations in the evolution rule. The relevance of this paper is to present that reversibility can be a useful structure to implement complex behaviors in cellular automata.